Math 6A ( Periods 1 & 2)

Ratios 5.1

A ratio is a comparison of two quantities. Ratios can be part -to -part, part – to -whole, or whole -to-part comparisons

The ratio of a to b can be written in three ways           

 a:b,                 a/b ,           and                           a to b.
Each of these is read “ a to b”

 Examples:

 2 red crayons  to 6 blue crayons
1 red crayon  for every 3 blue crayons
3 blue crayons for each red crayon
3 blue crayons per 1 red crayon
3 blue crayons out of every 4 crayons
2 red crayons out of 8 crayons

A tape diagram is a diagram that looks like a segment of tape. It shows the relationship between two quantities.

The ratio of your monthly allowance to your friend’s monthly allowance is 5:3 The monthly allowance totals $40. How much is each allowance?

To help visualize the problem, express the ration 5:3 using a tape diagram

You 

Your Friend

Because there are 8 parts, you know that one part represents 40÷8 = $5

5 parts represents 5 ∙5 = 25
3 parts represents 3 ∙5 = 15

Garlic bulbs- you separate 42 garlic bulbs into two groups: one for planting and one for cooking. You will plant 3 bulbs for every 4 bulbs that you will use for cooking. Each bulb has about 8 cloves. How many cloves will you plant?  To help visualize, express the ratio 3 for every 4 using tape diagram

Planting

Cooking

The seven parts represent 42 bulbs so each part represents 42÷ 7 = 6 bulbs

There are 3 ∙6 =18 bulbs for planting and 4 ∙6 = 24 bulbs for cooking.

The group of 18 bulbs has 18 ∙ 8 = 144 cloves. So you will plan 144 cloves of garlic.

Math 6A ( Periods 1 & 2)

 Finding Factors and Multiples  5-1


You know that 60 can be written as the product of 5 and 12. 5 and 12 are called whole number factors of 60. A number is said to be divisible by its whole numbered factors.

To find out if a smaller whole number is a factor of a larger whole number, you divide the larger number by the smaller.--- if the remainder is 0, the smaller number IS a factor of the larger number.

We set up T charts to find al the factors of numbers.
For example. Find all the factors of 24
24
1--24
2--12
3--8
4--6

When you go down the left side and back up the right you have
1, 2, 3, 4, 6, 8, 12, 24
all the factors of 24 in order!!!

A multiple of a whole number is the product of that whole number and ANY whole number. You can find the multiples of given whole numbers by multiplying that number by 0, 1, 2, 3, 4, ...and so on
The first five multiples of 7 are
0, 7, 14, 21, 28
because 0(7) = 0 ; 1(7) = 7 ; 2(7) = 14; 3(7) = 21; 4(7) = 28
... and put in set notation it would be
{0, 7, 14 ,21, 28}



If you were to ask for the first four NON-ZERO Multiples of 6
the answer would be 6, 12, 18, 24.. and in set notation
{ 6, 12, 18, 24}
Whereas the first four multiples of 6 ( you would need to include 0)
{0, 6, 12, 18}



Generally, any number is a multiple of each of its factors. That is, 21 is a multiple of 7 and it is a multiple of 3!!

Any multiple of 2 is called an EVEN number
A whole number that is NOT an even number is called an ODD number
Since 0 is a multiple of 2 .. that is 0 = 0(2) 0 is an EVEN number

What number is a factor of every number? ONE
Is every number a factor of itself? YES
What is ( are) the only multilpe (s) of 0? 0
How many numbers have 0 as a factor? only one number What number(s)? ZERO



The word factor is derived from the Latin word for "maker" the same root for factory and manufacture. When multiplied together factors 'make' a number.
factor X factor = product.